The present invention relates to equalizers used in, for example, data transmission systems to compensate for the effects of intersymbol interference in the received signal.
A fundamental challenge in transmitting a data signal over a wireless channel is to overcome the time-dispersive signal distortion caused by multipath propagation. Consider a multipath channel with a delay span—or delay spread—of τS microseconds, i.e., the span over which multipath components are received above the thermal noise floor. The channel dispersion thus spans L=RτS data symbols, where R is the data signaling rate in Mbaud. Roughly speaking, a value of L greater than unity, or perhaps less, will tend to introduce problematic intersymbol interference (ISI) in the detection process.
A variety of solutions are available to meet the demand for increasingly higher data rates in wireless communication systems in light of the multipath dispersion problem. These can be grouped into three general categories: 1) avoid large delay spreads, τS; 2) avoid large signaling rates, R; 3) accept both large τS and large R, but mitigate the resultant impact of multipath dispersion.
The first solution category involves limiting propagation distances and differential path delays by employing small cells, cell-sectorization, or beam-forming. For example, WLANs (wireless local area networks) based on the IEEE 802.11b standard are designed to operate indoors, where τS tends to be less than 100 ns. Such small delay spreads allow data rates up to 11 Mb/s (the highest rate of 802.11b) with little or no ISI-mitigation required.
The second category of solutions includes “orthogonal multiplexing,” which involves demultiplexing a high data-rate signal, with data rate RT, onto Nc orthogonal sub-channels, each with a signaling rate R=RT/Nc that is sufficiently small to avoid ISI (i.e., narrowband sub-channels or, effectively, long data symbols). Examples of this general concept are multicarrier modulation or multiple-input multiple-output (MIMO) antenna systems. MIMO systems have the added advantage of increased data rates without requiring large radio bandwidths. Moreover, equalization techniques can be combined with MIMO to allow greater signaling rates in each sub-channel. One important implementation is OFDM (orthogonal frequency division multiplexing), which is used in the IEEE 802.11a standard for WLANs, and also included in the draft standard IEEE 802.16 for WMANs (wireless metropolitan area networks).
The third category includes many possible solutions, but they are generally referred to as types of wideband single-carrier transmission with equalization. There are two key advantages of wideband single-carrier transmission. First, the energy of each data symbol is effectively spread over all frequencies within the signal band, which offers an inherent frequency diversity (or “multipath diversity”). In contrast, the narrowband signals in the first two categories above are inherently vulnerable to frequency-flat fading, and so interleaving and coding are usually required. Second, the modulation properties of single-carrier transmission—e.g., peak power and signal constellation (and also its associated coding)—can easily be controlled. In a channel with a relatively small path loss, for example, a large signal constellation (e.g., 16-QAM or higher) could be employed to allow high bit rates; and in a channel with a large path loss, coding or a small constellation—such as a two-symbol, biphase shift keying (BPSK) constellation or a four-symbol, quadrature phase shift keying (QPSK) constellation—could be employed to ensure reliable communication. Such an adaptive modulation scheme requires minimal feedback from the receiver. In orthogonal multiplexing schemes, on the other hand, a bank of somewhat independent modulators needs to be controlled and so more feedback is generally required, especially in frequency-division duplex links. Moreover, multicarrier modulation transmission tends to exhibit a higher peak-to-average power ratio than single-carrier transmission does, and so its transmit power generally needs to be backed off, to some degree, to control peak power and avoid transmit amplifier clipping.
The catch with single-carrier transmission is that it requires adequate equalization, or ISI mitigation, in multipath-dispersive channels. Conceptually, the most basic type of equalizer is linear—it convolves the received signal with a filter response that attempts to undo the convolution imposed by the multipath channel. The fundamental problem with linear equalization (LE), however, is that it cannot both eliminate ISI and provide optimal noise suppression with the same receive filter.
An improved structure in this regard is the decision feedback equalizer (DFE), which comprises both a receive (“forward”) filter and a feedback filter, whereby detected data symbols are convolved with the feedback filter response to effect ISI-cancellation. In this way, the forward filter can focus less on equalization, and more on noise suppression. It can be shown that the Shannon capacity of a single-carrier transmission link with an idealized decision-feedback equalizer (infinite-length optimal filters, and no error propagation) is equal to that of idealized multicarrier modulation (assuming equal power across the signal band). That is, given some specified schemes for adaptive modulation and error-correction coding, one would expect the performance and throughput of a decision-feedback equalizer in a single-carrier transmission system to be similar to that of multicarrier modulation with adaptive modulation/coding in each tone. The key difference is that single-carrier transmission can, in general, achieve that performance and throughput with less feedback from the receiver to the transmitter.
A conventional implementation of either linear equalization or decision-feedback equalization employs transversal filters, or tapped delay lines. The length, N, of such a filter is usually linearly proportional to the maximum value of L for which the equalizer is designed. The complexity per received symbol thus grows with N, or even with N2 for some adaptive equalizer implementations. Time-domain equalizer designs are thus becoming less attractive, or prohibitively complex, in applications that are seeing increasingly large values of L, e.g., in broadband wireless data networks.
An alternative is frequency-domain equalization (FDE), which is based on the concept of fast convolution. Fast convolution of a signal with some desired filter response involves a) transforming the signal into the frequency domain, via the FFT (fast Fourier transform); b) multiplying the transformed signal with the filter's frequency response; and c) transforming the resultant signal back into the time-domain, via the IFFT (inverse FFT). It also usually involves breaking the input signal into manageable blocks of length N symbols, where N is usually some power of two greater than the filter length. This, in turn, may call for block-overlap procedures at the IFFT output. Whatever the case, the complexity per output sample of this FFT-based convolution grows logarithmically with N, a modest growth compared with the linear growth of time-domain convolution. It turns out that for N≧32 this kind of frequency-domain filtering is generally a more attractive option than its time-domain counterpart.
The concept of frequency domain equalization—for the purpose of combating time dispersion—is almost 30 years old. It has found little application over that time, however, because most practical communication links exhibited limited dispersion, and so time-domain equalizers were adequate. Moreover, practical limitations of digital signal processing technology have, in the past, made large FFTs infeasible. More recently, however, demand for high-speed wireless data applications and advances in DSP/ASIC technology have stimulated new interest in frequency-domain equalization. In March 2001, both single-carrier transmission and OFDM modes were accepted in the IEEE 802.16 draft standard for fixed broadband wireless systems, where the single-carrier transmission mode has been designed to work with frequency-domain equalization. Either mode breaks the transmitted data stream into blocks of length N symbols and appends to each block a cyclic prefix, whereby N and the prefix length are chosen to be at least as large as the expected maximum value of the dispersion span, L. The prefix ensures that the corresponding received signal blocks appear to have a periodic property, which is essential for OFDM to operate and also allows single-carrier transmission with frequency-domain equalization to operate without the need for block overlap methods (which increase complexity).
In principle, the complexities of OFDM and single-carrier transmission-frequency-domain equalization are comparable (they both grow logarithmically with N), and the operating mode selected would likely depend on channel conditions. For example, single-carrier transmission-frequency-domain equalization may be preferred over OFDM in high path loss channels for which a small modulation constellation and large peak power are preferred to ensure reliable communication.
Most work on frequency-domain equalization over the years has analyzed linear structures. However, in the development of the 802.16 standard, a receiver was proposed by Falconer et al in “Frequency domain equalization for 2-11 GHz broadband wireless systems,” IEEE 802.16 Open Forum Tutorials, January 2001 that included a time-domain decision-feedback equalizer interworking with a linear frequency-domain equalizer, this combination being referred to as a frequency-domain decision-feedback equalizer (frequency domain DFE).
An equalization arrangement in which both the linear and decision feedback equalizers are realized in the frequency domain is disclosed in K. Berberidis and J. Palicot, “A frequency domain decision feedback equalizer for multipath echo cancellation,” Proc. Globecom '95, Singapore, December 1995, pp. 98-102. Such an approach permits the synthesis of long feedback filters with a much smaller increase in receiver complexity than is the case when the feedback structure is implemented in the time domain. The frequency domain outputs of the linear and decision feedback equalizers are each converted back into the time domain, whereupon they are combined and decisions as to the transmitted symbols are formed in response to the combined signal. The decisions thus formed are used not only as a final output, but also as the decisions fed back (after being first transformed into the frequency domain) to the decision feedback equalizer. A least mean squared algorithm is used to adapt, or update, the responses of the linear and decision feedback equalizers.